The era designations are just tools for kantei, in general swords looked like A in the Koto period and looked like B in the Shinto period. When you do Kantei there is only Koto and Shinto - if you bid on a Shinto smith for a Shinshinto maker they do not say "Wrong period". Of course we like to (need to) break it down further, most of the eras cited are political ones EG Nanbokucho and Muromachi while there are given dates for these periods swordsmiths did not change styles based on a specific date, rather they worked in the style of their teachers and perhaps followed trends seen in the capitals, only changing slowly and if you were out in the country you got the news much later.
The time periods are generalizations to help you break down all the tremendous data on makers into digestible bites and think in terms of trends. A smith who was born prior to the Haitorei and who worked primarily in the Shinshinto period is a Shinto smith. Born before the Haitorei but working primarily in the modern era = Gendaito smith. There will always be smiths that overlap these dates, some who are trendsetters and some who only follow the trend later...